The critical probability for random Voronoi percolation in the plane is 1/2

We study percolation in the following random environment: let Z be a Poisson process of constant intensity on ℝ², and form the Voronoi tessellation of ℝ² with respect to Z. Colour each Voronoi cell black with probability p, independently of the other cells. We show that the critical probability is 1/2. More precisely, if p>1/2 then the union of the black cells contains an infinite component with probability 1, while if p<1/2 then the distribution of the size of the component of black cells containing a given point decays exponentially. These results are analogous to Kesten's results for bond percolation in ℤ². The result corresponding to Harris' Theorem for bond percolation in ℤ² is known: Zvavitch noted that one of the many proofs of this result can easily be adapted to the random Voronoi setting. For Kesten's results, none of the existing proofs seems to adapt. The methods used here also give a new and very simple proof of Kesten's Theorem for ℤ²; we hope they will be applicable in other contexts as well. Research supported in part by NSF grant ITR 0225610 and DARPA grant F33615-01-C-1900 Research partially undertaken during a visit to the Forschungsinstitut für Mathematik, ETH Zürich, Switzerland     

Dehydration and dehydroxylation of reduced charge montmorillonite

Reduced charge montmorillonites (RCM) were prepared by the thermal treatment of lithiumsaturated montmorillonite. Samples prepared by mild thermal treatment with lithium contained more water sorbed than the original montmorrilonite. When RCMs were prepared, part of the lithium cations reacted with hydroxyl groups in the octahedral sheet and released protons, which reacted with the structure. Acid treatment probably enhanced the surface area. which was reflected in the amount of water sorbed. Deprotonation of hydroxyl groups was proved by the measurements of the ignition loss. The heating of lithium saturated montmorillonite at higher temperatures brough about the collapse of the interlayers and a decrease in the amount of water sorbed.     

Species differences in the metabolism of arsenic compounds

Humans are exposed via air, water and food to a number of different arsenic compounds, the physical, chemical, and toxicological properties of which may vary considerably. In people eating much fish and shellfish the intake of organic arsenic compounds, mainly arsenobetaine, may exceed 1000 μg As per day, while the average daily intake of inorganic arsenic is in the order of 10–20 μg in most countries. Arsenobetaine, and most other arsenic compounds in food of marine origin, e.g. arsenocholine, trimethylarsine oxide and methylarsenic acids, are rapidly excreted in the urine and there seem to be only minor differences in metabolism between animal species. Trivalent inorganic arsenic (AsIII) is the main form of arsenic interacting with tissue constituents, due to its strong affinity for sulfhydryl groups. However, a substantial part of the absorbed AsIII is methylated in the body to less reactive metabolities, methylarsonic acid (MMA) and dimethylarsinic acid (DMA), which are rapidly excreted in the urine. All the different steps in the arsenic biotransformation in mammals have not yet been elucidated, but it seems likely that the methylation takes place mainly in the liver by transfer of methyl groups from S-adenosylmethionine to arsenic in its trivalent oxidation state. A substantial part of absorbed arsenate (AsV) is reduced to AsIII before being methylated in the liver. There are marked species differences in the methylation of inorganic arsenic. In most animal species DMA is the main metabolite. Compared with human subjects, very little MMA is produced. The marmoset monkey is the only species which has been shown unable to methylate inorganic arsenic. In contrast to other species, the rat shows a marked binding of DMA to the hemoglobin, which results in a low rate of urinary excretion of arsenic.     

Electrochemical characterization of composite membranes based on crown-ethers intercalated into montmorillonite

Oxyethylene macrocyclic compounds (crown-ethers) act as ligands of intracrystalline cations of certain layered silicates as montmorillonites. Stable intercalation materials are formed which are used to prepare organic-inorganic membranes by encapsulating these intercalation compounds with a poly-butadiene thin coating. Electrochemical Impedance Spectroscopy (EIS) is used to study the resulting composite membranes in contact with aqueous electrolytes. From the impedance plots, the ionic resistance of the membranes is obtained. The thickness of the polybutadiene coating is an important factor determining the ability of ions to pass across the membrane. Marked differences in the ionic resistance are observed as a function of the nature of the interlayer macrocyclic compound. For non-intercalated montmorillonite membranes, the ionic resistance is strongly reduced, whereas for some crown-ether intercalated materials such as 18-crown-6 and dibenzo 24-crown-8, iono-selective membranes are obtained. Concerning the nature of the electrolyte, cations exhibiting greater hydration energies show higher difficulties to pass through the membrane and, consequently, the ionic resistance increases.     

Charge-transfer chromatographic study of the interaction of anticancer drugs with acetyl-β-cyclodextrin

The interaction between 23 anticancer drugs and acetyl-β-cyclodextrin (acetyl-β-CD) was studied by reversed-phase charge-transfer thin-layer chromatography and the relative strength of interaction was calculated. Acetyl-β-CD formed inclusion complexes with 16 compounds, the complex always being more hydrophilic than the uncomplexed drug. The inclusion forming capacity of drugs differed considerably according to their chemical structure. The significant linear correlation between the hydrophobicity and specific hydrophobic surface area of anticancer drugs indicated that they can be considered as a homologous series of compounds, however, their chemical structures are highly different.     

Parton-hadron duality in event generators

The validity of local parton-hadron duality within the framework of HERWIG and JETSET event generators is investigated. We concentrate one ⁺ e ^– annihilations in LEP 2 energy range as these interactions provide theoretically the cleanest condition for the discussion of this concept. We conclude that the concept of local parton-hadron duality is not valid in either of the two generators considered.     

Unexpected end‐groups of poly(acrylic acid) prepared by RAFT polymerization

Low‐molecular‐weight poly(acrylic acid) (PAA) was synthesized by reversible addition fragmentation chain transfer polymerization with a trithiocarbonate as chain‐transfer agent (CTA). With a combination of NMR spectroscopy and matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry, the PAA end‐groups of the polymer were analyzed before and after neutralization by sodium hydroxide. The polymer prior to neutralization is made up of the expected trithiocarbonate chain‐ends and of the H‐terminated chains issued from a reaction of transfer to solvent. After neutralization, the trithiocarbonates are transformed into thiols, disulfides, thiolactones, and additional H‐terminated chains. By quantifying the different end‐groups, it was possible to demonstrate that fragmentation is the rate limiting step in the transfer reaction. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5439–5462, 2004     

On theK-property of some planar hyperbolic billiards

TheK-property is demonstrated for a class of planar billiards satisfying Wojtkowski's principles. Their boundary may consist of convex-scattering, concave and linear pieces. Earlier Wojtkowski showed that these billards had non-zero Lyapunov exponents.     

Synchronization Analysis of Coupled Noncoherent Oscillators

We present two different approaches to detect and quantify phase synchronization in the case of coupled non-phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the R?ssler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators.     

Use of new composite materials for the determination of Cu, Cd, Mo, As, and Sb in biological samples by radiochemical neutron activation analysis

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